In recent years, Lagrangian Coherent Structures (LCS) have been characterized using the Finite-Time Lyapunov Exponent, following the advection of a dense set of particles into a corresponding flow field. The large amount of particles needed to sufficiently map a flow field has been a non-trivial computational burden in the application of LCS. By seeding a minimal amount of particles into the flow field, Moving Least Squares, combined with FTLE, will extrapolate the important feature locations at which further refinement is desired. Following the refinement procedure, MLS produces a continuous function reconstruction allowing the characterization of Lagrangian Co- herent Structures with a lower number of particles. Through multiple data sets, we show that given a sparse and refined sampling, MLS will reproduce FTLE fields exhibiting a nominal error while maintaining a performance increase when compared to the standard, dense finite difference approach

As computational capabilities increasingly outpace disk speeds on leading supercomputers, scientists will, in turn, be increasingly unable to save their simulation data at its native resolution. One solution to this problem is to compress these data sets as they are generated and visualize the compressed results afterwards. We explore this approach, specifically subsampling velocity data and the resulting errors for particle advection-based flow visualization. We compare three techniques: random selection of subsamples, selection at regular locations corresponding to multi-resolution reduction, and introduce a novel technique for informed selection of subsamples. Furthermore, we explore an adaptive system which exchanges the subsampling budget over parallel tasks, to ensure that subsampling occurs at the highest rate in the areas that need it most. We perform supercomputing runs to measure the effectiveness of the selection and adaptation techniques. Overall, we find that adaptation is very effective, and, among selection techniques, our informed selection provides the most accurate results, followed by the multi-resolution selection, and with the worst accuracy coming from random subsamples.

Fluid mechanics considers two frames of reference for an observerwatching a flow field: Eulerian and Lagrangian. The former isthe frame of reference traditionally used for flow analysis, and involvesextracting particle trajectories based on a vector field. Withthis work, we explore the opportunities that arise when consideringthese trajectories from the Lagrangian frame of reference. Specifically,we consider a form where flows are extracted in situ and thenused for subsequent post hoc analysis. We believe this alternate,Lagrangian-based form will be increasingly useful, because the Eulerianframe of reference is sensitive to temporal frequency, andarchitectural trends are causing temporal frequency to drop rapidlyon modern supercomputers. We support our viewpoint by running aseries of experiments, which demonstrate the Lagrangian form canbe more accurate, require less I/O, and be faster when compared totraditional advection.